Abstract
In this paper, we study the following $p(x)$-biharmonic problem in Sobolev spaces with variable exponents \begin{equation} \begin{cases} \triangle ^{2}_{p(x)}u=\lambda ({\partial F } (x,u)/{\partial u}) & x\in \Omega , \\ {\partial u}/{\partial n}=0 & x\in \partial \Omega ,\\ {\partial }(|\triangle u|^{p(x)-2}\triangle u)/{\partial n} =a(x)|u|^{p(x)-2}u & x\in \partial \Omega . \end{cases} \end{equation} By means of the variational approach and Ekeland's principle, we establish that the above problem admits a nontrivial weak solution under appropriate conditions.
Citation
Mounir Hsini. Nawal Irzi. Khaled Kefi. "Eigenvalues of some $p(x)$-biharmonic problems under Neumann boundary conditions." Rocky Mountain J. Math. 48 (8) 2543 - 2558, 2018. https://doi.org/10.1216/RMJ-2018-48-8-2543
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